On uncertainty quantification via the ensemble of independent numerical solutions

Alekseev, A. K.; Bondarev, A. E.; Kuvshinnikov, Artem E.

doi:10.1016/j.jocs.2020.101114

Cited by 18 publications

(19 citation statements)

References 16 publications

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“…A large number of different applications of a generalized computational experiment are described in detail in [16][17][18][19][20][21][22][23][28][29][30]. The concept of a generalized computational experiment was applied to a wide range of both model and practical problems.…”

Section: Generalized Computational Experimentsmentioning

confidence: 99%

“…Since different solvers implement different numerical methods, the errors were markedly different from each other. The initial and boundary conditions, as well as the settings of the solvers, were set similarly to [26,28]. Fig.…”

Section: Comparative Accuracy Estimation Using Reference Solutionmentioning

confidence: 99%

“…The concept, basic methods and approaches of a generalized computational experiment, as well as a number of software tools for its implementation were developed in Keldysh Institute of Applied Mathematics RAS. The main aspects of constructing a generalized computational experiment and examples of its implementation are described in detail in [16][17][18][19][20][21][22][23][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

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On the construction of a generalized computational experiment in verification problems

Alekseev¹,

Bondarev²,

Галактионов³

et al. 2020

MathMon

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This work is devoted to the application of a generalized computational experiment for a comparative assessment of numerical methods accuracy. A generalized computational experiment allows one to obtain a numerical solution for a class of problems determined by the ranges of defining parameters variation. The applications of such approach in the presence of a reference solution and in its absence are discussed. An example of error surfaces constructing is given when the solvers of the OpenFOAM software package are compared. The classic inviscid problem of oblique shock wave is used as a basic task. Variations of the key parameters of the problemthe Mach number and angle of attackare considered. In addition to the OpenFOAM solvers, the comparison included the WW method, which has a second order of accuracy in time and space and an adjustable artificial viscosity. The problem of flow around a cone at an angle of attack with varying Mach number, cone angle and angle of attack is also considered. The concept of an error index is introduced as an integral characteristic of deviations from the exact solution for each solver.

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Section: Generalized Computational Experimentsmentioning

confidence: 99%

Section: Comparative Accuracy Estimation Using Reference Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the construction of a generalized computational experiment in verification problems

Alekseev¹,

Bondarev²,

Галактионов³

et al. 2020

MathMon

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show abstract

“…Being computationally efficient and memory saving, the scheme was proved to be unconditionally stable, being the implementation based on the single-component system, and does not required to choose a reference species for multicomponent fluids. In the same context, Alekseev, Bondarev, and Kuvshinnikov [ 22 ] proposed an instance of epistemic uncertainty quantification concerning the estimation of the approximation error norm is investigated using the ensemble of numerical solutions obtained via independent numerical algorithms. The ensemble of numerical results obtained by five OpenFOAM solvers is analyzed.…”

Section: Overview Of the Virtual Special Issuementioning

confidence: 99%

Computational Science in the Interconnected World: Selected papers from 2019 International Conference on Computational Science

Cardoso

Rodrigues

Monteiro

et al. 2020

Journal of Computational Science

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“…Another branch of nonstrict a posteriori error estimation methods has a non-intrusive form of certain postprocessor that significantly reduces efforts for coding and debugging. It may be based on the Runge rule [5], Richardson extrapolation (RE) [13,14], Inverse Problem based approach (IP) [15] or ensemble based methods (EM) [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Nonstrict methods for a posteriori error estimation

Bondarev

Alekseev

2020

CPT2020 the 8th International Scientific Conference on Computing in Physics and Technology Proceedings

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The paper is devoted to comparison of a posteriori methods (based on the precomputed solutions) for approximation error estimation. Rigorous a posteriori error estimation for computational Fluid Dynamics at present is practically impossible due to nonlinearity and the discontinuities that may occur and migrate along the flow field. In this situation, several nonstrict (weak) forms of a posteriori estimation of the approximation error may be considered. They either do not provide the error norm estimation in the form of inequalities or provide values of the effectivity index to be less than unit. The best quality of estimates are provided by the Richardson extrapolation, unfortunately for the cost of extremely high computational burden. We pay the special attention to the nonstrict methods that either cannot be presented in a form of inequalities, or demonstrate the effectivity index of an estimator to be below unit. Several new, computationally inexpensive methods for both the point-wise error and the error norm estimation are considered. They are nonintrusive, realized by postprocessing and provide a successful compromise of the reliability and computational efforts. Methods based on the use of an ensemble of independent solutions can be implemented by constructing a generalized computational experiment, which sharply increases the speed and efficiency of the assessment.

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On uncertainty quantification via the ensemble of independent numerical solutions

Cited by 18 publications

References 16 publications

On the construction of a generalized computational experiment in verification problems

On the construction of a generalized computational experiment in verification problems

Computational Science in the Interconnected World: Selected papers from 2019 International Conference on Computational Science

Nonstrict methods for a posteriori error estimation

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